Machine-Learning Non-Conservative Dynamics for New-Physics Detection

TL;DR

This paper introduces NNPhD, a neural network-based method for detecting non-conservative forces indicating new physics by decomposing force fields, with demonstrated success in various numerical experiments and improved future state prediction.

Contribution

The paper presents a novel neural network approach to identify non-conservative forces, enabling new physics discovery through force decomposition and phase transition analysis.

Findings

Successfully rediscovered friction, Neptune, and gravitational waves from data.

Identified a phase transition at λ=1 for force decomposition.

Outperformed previous methods in predicting damped double pendulum dynamics.

Abstract

Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our Neural New-Physics Detector (NNPhD) aims to detect new physics by decomposing the force field into conservative and non-conservative components, which are represented by a Lagrangian Neural Network (LNN) and a universal approximator network (UAN), respectively, trained to minimize the force recovery error plus a constant $\lambda$ times the magnitude of the predicted non-conservative force. We show that a phase transition occurs at $\lambda$=1, universally for arbitrary forces. We demonstrate that NNPhD successfully discovers new physics in toy numerical experiments, rediscovering friction (1493) from a damped double pendulum, Neptune from Uranus' orbit (1846) and gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD coupled with an integrator outperforms previous methods for predicting the future of a damped double pendulum.